Totally depends on their strategy! Some L/S funds run pair trades, some just roll SPX puts, some are totally idiosyncratic. In most cases, they try to hedge out equity market beta and try to be market neutral (but again, depends on strategy… Einhorn or Pershing Square are likely not market neutral).
Sorry I wasn’t clear, I meant each short position is about 1 to 2% of NAV. In total they might have 0 to 50 individual short positions, which would complement their long book. You’d look at their net and gross position to see their directional positioning and leverage. E.g. if they are 50% net long with 150% gross, it’s likely that they have 100% long and 50% short.